The goal of this study is to demonstrate the safety and efficacy of arimoclomol in people with rapidly progressive forms of familial amyotrophic lateral sclerosis (ALS) due to mutations in the superoxide dismutase-1 (SOD-1) gene. ALS is an inexorably progressive and fatal neurodegenerative disorder for which there is no effective therapy. Familial ALS due to specific mutations in the SOD1 gene (e.g., A4V) is a very rapidly progressive form of the disease that is characterized pathologically by the accumulation of SOD1-containing aggregates within both neurons and astrocytes. Mutant SOD1 reduces the activity of heat shock proteins and thereby permits the formation of protein aggregates that constitute these neuronal and astrocytic inclusions. Arimoclomol, a co-inducer of heat shock protein gene expression, promotes de novo protein folding, facilitates repair of misfolded proteins and targets misfolded proteins for degradation. In addition to its targeting a pathogenic mechanism in SOD1 positive familial ALS, arimoclomol significantly prolongs survival in the SOD1 mouse model of ALS, even when administered after the appearance of clinically manifest disease. Furthermore, arimoclomol has proven safe and tolerable in a Phase 2a study of patients with sporadic ALS, it crosses the blood-brain barrier and exhibits a dose-dependent increase in cerebrospinal fluid (CSF) concentration. This seamless, adaptive, Phase 2/3 randomized, double-blind, placebo-controlled trial will enroll approximately 80 participants in two stages. The first stage will include 30 participants followed monthly over a period of 6 months. Results of this first stage will be used to determine safety, tolerability, futility and potential efficacy of arimoclomol. The analysis of this stage-1 data will also be used to re-estimate the sample size required for the second stage of the study that will include approximately an additional 50 subjects, followed over a period of 12 months. Participants in stage-1 will continue to be followed for an additional 6 months in stage-2. The primary outcome measure is the change in the revised ALS functional rating scale (ALSFRS-R) between baseline and the month-12 visit. Secondary outcome measures include time to tracheostomy or permanent assisted ventilation, forced vital capacity, negative inspiratory force, strength, long-term safety and tolerability of arimoclomol as well as motor unit number estimates.